How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm?
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Answered by
10
The volume of the rectangular solid lead will be the same as that of all the spherical lead shots.
Assuming internal dimensions.
Volume of rectangular solid = length * breadth * height = 66 * 42 * 21 cm^3 = 58212 cm^3
Volume of the sphere = 4/3 * r^3
Given r = 4.2/2 = diameter/2 = 2.1
Let n number of spherical shots were made.
=> n * Volume of spherical lead shots = Volume of rectangular solid
=> n * 4/3 * r^3 = 58212 (from 1 above)
=> n * 4/3 * 2.1 * 2.1 * 2.1 = 58212
=> n = 4714 approximately.
Assuming internal dimensions.
Volume of rectangular solid = length * breadth * height = 66 * 42 * 21 cm^3 = 58212 cm^3
Volume of the sphere = 4/3 * r^3
Given r = 4.2/2 = diameter/2 = 2.1
Let n number of spherical shots were made.
=> n * Volume of spherical lead shots = Volume of rectangular solid
=> n * 4/3 * r^3 = 58212 (from 1 above)
=> n * 4/3 * 2.1 * 2.1 * 2.1 = 58212
=> n = 4714 approximately.
Answered by
12
Let number of headshots be x.
Volume of lead in the rectangular solid =(66×42×21)cm3
Radius of a lead shot = 4.2/2 cm = 2.1 cm
Volume of a spherical lead shot = 4π×(2.1)3cm3
Volume of x spherical lead shots =
= [(4/3) × (22/7) × (2.1)^3 × x )] cm^3
Volume of x spherical shots = Volume of lead in rectangular solid
(4/3 × 22/7 × (2.1)^3 × x ) = 66 × 42 × 21
⇒ x = 66 × 42 × 21 × 3 × 7/4 × 22 × (2.1)^3
⇒x = 1500
∴ Number of lead shots = 1500
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